Modeling Interactions Between Cities to Simulate Urban Hierarchies

In certain generative models of hierarchical systems of cities with scale invariance properties, the processes modeled are placed at the level of the cities themselves, their competition and complementarity, and their exchanges in terms of goods, information or population. Three categories of processes related to the functioning of cities as systems are at the root of urban scaling laws: spatial interactions between cities, the functional specialization of cities associated with the spatial division of labor and the hierarchical diffusion of innovations. The changes in the modeled systems of cities cover a wide range of time periods and scales: from a few decades to a few centuries, from ancient times to the present day. The functional diversification of cities over time can therefore result from the redistribution of existing activities and functions between cities (relocation process) or their multiplication in situ (endogenous socioeconomic growth).